10 papers
Stable Degeneration, Non-degenerate Forms, and Kaledin's Conjecture
Chenyang Xu, Ziquan Zhuang, Henri Guenancia
We prove that stable degeneration, the canonical degeneration associated to the normalized volume minimizer of a Kawamata log terminal (klt) singularity, preserves non-degenerate r…
Kähler-Einstein metrics of negative curvature
Henri Guenancia, Ursula Hamenstädt
Given any integer , we construct a compact Kähler-Einstein manifold of dimension n of negative sectional curvature which is not covered by the ball.
Families of singular Kähler-Einstein metrics
Eleonora Di Nezza, Vincent Guedj, Henri Guenancia
Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Kähler manifolds, that al…
A complex analytic approach to orbifold Chern classes on singular varieties and its applications
Henri Guenancia, Mihai PÄun
In this article, we prove the orbifold version of the Bogomolov-Gieseker inequality for stable -sheaves on Kähler varieties, generalizing our earlier work \cite{GP25} i…
Kähler-Ricci flows coming out of metric spaces
Alix Deruelle, Vincent Guedj, Henri Guenancia +1
Given a compact Kähler manifold and a closed, positive -current on , we find sufficient conditions for to induce a metric structure which is the Gr…
Beauville-Bogomolov decomposition for klt varieties
Henri Guenancia
These lecture notes present a mostly self-contained proof of the singular version of Beauville-Bogomolov decomposition theorem for compact Kähler varieties with log terminal singu…